The fascinating patterns shown in cast # 34 were found in a quarry at Westerstetten (near Ulm, S.Germany). They drape a huge block of Upper Jurassic limestone that had fallen into a clay-filled fissure. This is surprising, because karst fissures are the result of limestone dissolution, while the micritic crust bearing these ornaments originated certainly by in-situ  precipitation. Even though the origin of these sculptures is still problematic, they clearly belong to the family (morphospace) of zebra patterns that are found in very disparate situations.

In the inorganic world, wave ripples (#3) are an example. Here, the distance between crests depends on the distances that sand grains roll to and fro during one wave. Similar, but less linear, patterns emerge in a framed layer of water between glass plates when it is warmed from below.  In this case the instability releases convection rolls (Bénard cells), whose diameters depend on the distance between the glass plates. Much larger convections cells in the mantle of our planet appear to be responsible for plate tectonics. Similar spiral or meandering patterns originate in fluids, in which a chemical reaction proceeds in a rhythmical fashion, or in the magnetic domains of a garnet crystal. Other examples are load casts, in which heavy sand has sunk into a soft mud layer underneath, but without alignment.

                      In the organic world examples of zebra patterns are just as diverse. They reach from brain corals to fur colors and from shell ornaments to the patterns on our own finger tips. The latter have the function to increase the grip and to regulate the distribution of sweat glands and sensory cells in the skin. For these functions, the particular pattern of grooves and ridges is irrelevant, which explains variability comparable to that of the Bénard cells in our experiments. It is a strange paradox that our most unmistakeable identity does not rest on heredity, but on the randomness of a self-organizational process!

                      While these comparisons alone do not explain the Westerstetten sculptures, they make an inorganic origin very likely.

Whether or not this fascinating sculpture qualifies as an object of art is another question.

The work of a modern artist # 35 illustrates the flexibility of the term. Similarly, masons in the royal summer palace near Beijing used another self-organizing process ("figures de viscosité") to ornament the floor tiles on the pathway. They lifted the top panel of the mould while the cement was still sticky. The result is intriguing dendritic ridge patterns that are different in every tile.

So where is the limit?

Are you an artist when your hand creates patterns in the glass panel?

Were the Chinese masons artists when they used a self-organizing process to produce a pleasing design?

Should the definition of art not be based on perception rather than fabrication?

The true nature of the Westerstetten sculptures (# 34) can be better understood by comparing with a phenomenon that is expressed not by relief, but as color bands in vertical sections through the rock. These "Liesegang Rings" are most beautifully developed in the ancient city of Petra, Jordan, where the Nabataeans carved the precipitous walls of a natural labyrinth into impressive tomb facades in the last centuries b.c.

We know that Liesegang Rings formed long after the origin of the rock by ground water permeating gradually through the pore space. In this process, soluble constituents are taken up and re-precipitated along the advancing front as soon as a critical concentration has been reached. This explains the regularity of the rings, but not their geometry. Why the fronts are so smoothly curved and why did they fail to develop larger diameters?

The first question can only be answered by analogy. The rings are sections through three-dimensional surfaces resembling balloons or biological structures shaped by hydrostatic pressure. Accordingly the advancing cementation front must have had the property of a tensile membrane, inside which a differential pressure could build up osmotically. Such a membrane could have been formed by the precipitate itself, but it is also possible that bacteria were involved, whose presence in deep rocks has recently been demonstrated. The size of the balloons would again be limited by a threshold concentration of the dissolved salts, at which growth was stopped by precipitation. As these salts had come from outside, the balloons should become larger where the rock around was impoverished in nutrient salts.

This view can be tested, and linked with the Westerstetten sculptures (# 34), by our second peel from Petra (# 34 b). Here an early system of Liesegang Rings started from a small bubble-shaped nucleation center. Further growth proceeded along the bedding plane by the addition of the concentric balloon rings (with internal growth lines) that resemble the 3-dimensional Westerstetten sausages. The upper margin even shows the white "eye" in the center that is also characteristic for the Westerstetten systems and for similar overgrowths on chert concretions from arid climates. Another significant feature is the increase of sausage cross sections away from the center of the Petra concretion. Still larger diameters are reached in the sheet-like envelopes that formed later on top and particularly in the ”shadow” of this concretion. .

If the involvement of endolithic bacteria could be confirmed, the shapes of concretions, Westerstetten sculptures and Liesegang Rings may be even biologically mediated. Nevertheless they are controlled by rules of self-organization rather than genomically coded programs. Such processes, however, should also interest evolutionary biologists, because they often provide the raw material on which Darwinian selection can start to operate.